Reflection on Blogging March 8, 2012

 

Blogging was a very new experience for me as I don’t have Face book or twitter account and mainly only use Email for work until this year. This class has not only taught me how to teacher Algebra to my students but also has taught me a lot about using the computer. I was able to learn how to access my friend’s blogs though my account and make comments. I still don’t understand fully the use of categorizing and tagging the blog as it doesn’t group like categories together. I do understand the difference between a page and a new blog but don’t know if there is etiquette for use. Adding pictures was frustrating as it wouldn’t accept them unless they were saved as web page. Also diagrams I drew using shapes were impossible to copy. Blogging is a good way to communicate and share information probably better than in a classroom setting because you read everyone’s assignment and comments, and can add comments yourself, going away with a lot of ideas. In the classroom there just isn’t enough time for all of this interaction.   This class has helped me see the big picture of math beyond just being able to do the computations.  Through this class I have learned that math can be an interactive hands on class that can be relate to real world living.  This is something I am very apprehensive about in becoming a math teacher because I have taught a FACS for 32 years. I found the entire class very interesting, although I think I enjoyed the linear equations and patterns the best. For the 1^st time I was able to relate to word problems as they were related to patterns which make it come to life for me. These were skills I apply in everyday life without realizing the math concept involved.  I did like and see the value to journals and would like to have students do them in a blog. Blogging them might reduce the resistance that the students have towards writing in math. I don’t know the district stand on Blogging, but they do allow Edmodo, which seems very singular but I think blogging is safer. I will also continue to use my blog to access resources and store others as I see my entire blog as a resource for teaching math.

Factoring Quadratics in My Own Words

Factoring Quadratics in Your  Own Words

 

The factoring of quadratics is done to simplify the equation. You are taking a trinomial and changing it to a binomial.  The formula for a Quadratic is ax² +bx +c.

1^st look at c and determine its’ factors. Choose the two factors whose sum equals b (7).

Example: x² + 7x+ 12       factors of 12 (1*12) (2*6) (3*4). 3+4 =7 so this is the one.)

2^nd Look at the first term in the equation, (ax²)and divide by 2.

Example x² = x * x

Now put the parts together in a binomial (x+3) (x+4).

It did make me internalize the concept because I had to explain it. It is like teaching to one’s self. This activity could be incorporated in the journal, having them paraphrase a definition, a process or simply what they learn that day will help them learn and remember the concept because it is a form of teaching only to oneself.

Evalutating My Definition Functions and Equations February 18, 2012

After reading everyone’s definitions of functions and equations they all have the basic definition or revised it to such. My own definition for functions could be elaborated to include that the functions are  what  (the numbers) are plotted on a coordinate plane graph. And possibly give more examples of equations.

In the classroom to ensure the students understand the difference I would use visuals when explaining the two, pointing out likes and differences using a Vin diagram. Then conduct a scavenger hunt, that encompass all 4 team members classroom. I would us index cards and write functions on half and equations on the other half. Each student would have to find 2 of each within  the next 24 hours. In class the next day have then present their finding to class and determine their accuracy.

Applets

Applets

 

First off let me say I am not much of a game person. In reviewing the sites some were very frustrating because either I didn’t understand the directions or there was not any feedback. The function machines and some of the graph makers could be corporate as an interactive visual as you are explaining the topics, thus making the lesson more interesting. The illuminations Site  offered something called Dynamic Paper which allow you to create graphs, graph paper and geometrical shapes for use in you classroom on assignments you generated. http://illuminations.nctm.org/ActivityDetail.aspx?ID=205

The applet I likes the best was The Hanoi Towers. At first I saw it as impossible to move the stack of disc from one place to another with the two rules they imposed: one disc at a time and you couldn’t put a bigger disc on top of a smaller one. So I started on the easiest level and worked my way up. Then it became a challenge, once you got the strategy down it became easier. I would use this lesson at the beginning of Equations and Functions to show the students that every problem has a pattern and solution to solve the pattern it just takes some careful analysis of the problem. Perhaps we would even revisit this activity if students became frustrated as the lessons move to more complicated functions

http://nlvm.usu.edu/en/nav/frames_asid_118_g_3_t_2.html?from=category_g_3_t_2.html

The Magic of Proportions February 16, 2012

The Magic of Proportions

Mary is making peanut fudge as a treat for her 1st grade students; they have been working very hard on learning their new vocabulary. Since they are learning about words that end in “udge´ she chose fudge. She has a total of 50 students in 3 classes. She would also like some extra for the teacher’s room. The recipe is as following

⅓cup peanut butter

½ lb. butter

1 lb. box 10x sugar

⅓ cup dried milk

⅓ cup corn syrup

1 tbsp.  Water

1 teasp.  Vanilla             serves 16- 2’ pieces

Figure out how many recipes she needs to make. (4) to give you 64 pieces. Calculate the new measures for each ingredient using proportions.

16    64           ⅓   ×  64     21.

― =     ―            ―     ―    =  ―        =1.33 cups or 1⅓ cups peanut butter

⅓      x              16 ×  x         16x

The bag of chips that Johnny just devoured the whole thing, says the sodium amount is 95mg per the 20 chip serving. The bag contains 80 chips. How much sodium did Johnny consume?

20                80            95     80   7600

―         =     ―    =      ―     ―   =   ―          =380mg sodium in 80 chips  3 ¾ oz. bag

95mg             x           20     x        20x

If the total fat content is 9grams per serving of 20 chips, how much fat did he consume in eating the 80 chips?

Equations and Functions in Your Own Words February 15, 2012

Equations and Functions in Your Own Words.

 

Function is when you take a variable for x and plugged it into the equation and get I result. The function machine takes a number in, knows the equation, and puts out a new number out (y). Or simply what is done to a number to make it another number.

If f(x) =2   then in 4x-4          If f(x) = 3   then 4x-4                 If f(x) = 4   then 4(x)-4

4(2)-4                                                                    4(3)-4                                                    4 (4) -4

8-4 =4                                                                    12-4=8                                                  16-4=12

F(x) =4                                                                 F(x) =8                                                  F(x) =12

                                                                                                                                                                                                                                                                                                

                                                                                   3

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07s104.jpg

raider.mountunion.edu

Equation in the algebraic problem, 4x-4=y. It is similar to the expression but must equal something.

Supplemental Activities

Journal blog assignment

Complete in journal. Show all work equation table function. Try to graph results.

At school you are in a jump rope -athon to raise money for the Heart Association.  Your sponsors have pledged to give you $3.00 for every 30 minute session of jumping you complete, plus a $.25 bonus if you don’t miss during the session. Assume you never miss, how much will each sponsor owe if you jump 3 sessions?  4 session? 5 session?

5 sessions?

Web based tutorial activities and games.

http://www.ixl.com/math/grade-8

http://www.mathwarehouse.com/algebra/relation/math-function.php

http://www.coolmath.com/algebra/15-functions/01-whats-a-function-domain-range-01.htm

http://www.math-play.com/Algebra-Math-Games.html

Math Myths February 11, 2012

My Reflections of Math Myth

 

 

Several of these Math Myths were believed when I was going to school. The main one I remember was the memorization of math facts was crucial .I wasn’t until I started teaching that I noticed this myth was no longer adhered to. Students had to “learn” and not memorize the information. It took me a while to figure out the difference between learning and memorizing, because when I was in school there was little real life relevant connection provided or purpose to the learning. Children were taught to do as they were told and not to question. Counting on your finger was not allowed and in Catholic school would earn you a smack across the knuckles.  Today they are considered a manipulative. It was also a general belief that some people had a “Math Mind”, while others didn’t. When my own sons were in school, being able to complete 100 problems in a minute was key to placement in a math class, which supports the myth good math students, do math problems quickly. Fact is math problems take time to think out and solve. Some of us need more than others.

A lot has changed in schools and teaching, math in particular since I was in school 37 years ago. The biggest change came with the installation of the State Standards in the mid 90’s. They demand a higher level of thinking on the student’s part and the teachers. These standards were brought about by demands of the National Mathematics Associations in responds to demands for predicted as needed to live in the 21^st centenary world.

We as educators must encourage all student and provide for them to reach success. Even if it is one small step at a time, as forward is the goal. It is not easy to change a person’s attitude let alone societies.  The main thing is to provide relevance to our teaching. Two ideas that stood out to me during the reading were having students tutor others, struggling students could tutor young grades. Involving parents by having them require their child to teach (or refresh their memory) what they learned that day. This not only gives encouragement to the student but is considered the highest level of learning: to be able to teach it. Journaling would be a great way to find out the students career goals and an angle for the teacher to use in motivating them. Also having quest speakers take can relate how math connects with their career.

Translating Pattern Narrative into Formal Math language February 10, 2012

 

 

 

 

Pascal’s Triangle

Pascal’s triangle is an equilateral triangle consisting of positive integers. The perimeter of the two legs and the vertex angle are all 1’s.  The size can go small and as great as infinite by adding 1 to the outer legs at the base. The base is made up of the sum of the pattern rule. The integers in the entire perimeter are highlighted. All the integers form a straight line on the diagonal, but not vertically or horizontally. Not all rows have an integer on the altitude line.

The integers on each horizontal row are symmetrical from center to edge.

Along with the base line being highlighted, other integers are highlighted.  The highlighted  integers that encompass the bottom rows running parallel with the base form two small triangles with a larger inverted triangle in the center.  This triangle consists of odd numbers. Two smaller triangles highlighted in the top section consist of prime numbers.

The pattern is as follows:

Starting at the top right of the vertex is row 0 consisting of ones. It runs diagonally to the lower left.  Row 1 consist of counting numbers 1-15, representing the sum of 1 plus it diagonal to form the next number. 1 + 1= 2 .The numbers in the following rows  arethe sum of the two numbers on the diagonal line above the sum.

 

                

 

 

 

 

 

 

 

The formula is a invert triangular shape. Therefore the sums are triangular numbers. The formula works in any direction and any combination of the inverted triangle.

Non Linear Web Quest February 9, 2012

Non Linear Web Quest

   

 

 

                     

 

 

Fibonacci

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

Great site. Provides walk through explanations and activities that apply Fibonacci formula to all things in nature that are non linear. Photographs are excellent, giving real life examples. . Also includes activities on the Golden Rule.

The Golden Ratio

http://cuip.uchicago.edu/~dlnarain/golden/activities.htm

This sight has interactive learning on the “Golden Ratio. Where it is in nature, Art and Architecture. It works you though how to construct a golden rectangle. Colorful and easy to read.

Prime Numbers

http://www.softschools.com/math/prime_numbers/prime_numbers_up_to_100/

Provides simple games for identifying prime numbers.

Arranged by grade level.

All topics in math for 7^th grade. Offers quizzes, worksheets and games.

Pentagram

http://www.angelfire.com/id/robpurvis/pentagram.html

I found this information interesting, I never thought of a pentagram in terms of a human. I guess that is why we are all shining stars.

• Were there ideas or concepts you were not familiar with? What were they?

I had never really thought of any of the things in nature as mathematical. Great realistic ideas to use within the classroom. Nor have I thought of a human in pentagram form although I have seen this picture before.

• What images did you find particularly striking?

I found the snail shell the most fascinating. I spend a lot of time looking for shells; those are hard to come by.

• Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?

Plants, figurines, pictures of people, acorns.  Celtic knot ring, Celtic spiral wind chine, foods, and the design on the wall in my computer room (son’s old room.) It is sponge painted, randomly throwing method plus hand prints.

• How can you adapt this web quest activity for your classroom?
• If I interpreted the assignment correct than students could do a web quest on any topic and always come away more informed the before they started.

Working With the Definition of Linear Patterns February 8, 2012

Working with the Definition of Linear Patterns

My definition

A Non- traditional pattern is a pattern but it does not repeat regularly in any order. Some fabrics and wallpapers are like this.

Formal Definition

”Non-traditional patterns are simply patterns that do not follow a repetitive format.”

From Teaching Algebra to Middle School Students, Module 4-A, Key Information):

Kid friendly definition

Linear pattern– It is a form of displaying data collected. Look for what they repeated to get the new number.  This is the pattern. You must figure out the amount that the first number has changed. If 1 is 10 than 2 is 20. The variable is what you did to get the sum or product. In this case, the variable is ×10. # of cd’s × v = Total cost.

X                            y

# of   cd’s	Total   cost
1	10
2	20
3	30

Formal Definition

Linear Pattern-When a pattern in a number sequence in added or subtracted by the same number every time.

Read more: http://wiki.answers.com/Q/What_is_the_definition_of_a_linear_pattern#ixzz1liFp2Ght

Comparison- I state a pattern is something that repeats, which could be a number. They state the number sequence is always change by the same number, which is a form of repetition. You are always adding, subtraction or multiplying by the same number. I refer to the number that you always multiply as a variable. I feel their definition is simpler to the point, but mine has visuals.

So it goes without saying that I feel the best way for to help students learn the formal definition is to provide them with visuals and/ or have them experience working with a pattern for a purpose.  Using examples of patterns that are familiar to the students already would help in the understanding. While exploring online examples of linear patterns I came across a simple example about chairs around a square table, and how many chairs would you need if you had 25 tables. It was labeled for 3-5 grades, but I think for an introduction activity used to try to get the students to understand the definition, it was great. It could also be tweaked to make it a harder problem by using round or rectangle tables. What I liked best is the students could actually act out the problem by using the desk and chairs in the classroom. To draw in the girl’s interest I saw an example on making knot bracelets or beaded necklaces.